鞅分析在最优投资与消费策略中的应用  

Application of Martingale Analysis to Optimal Investment and Consumption Strategies

作　　者：邵正伟[1] 孔繁亮[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2008年第2期119-122,共4页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金项目资助(10371027);黑龙江省教育厅科研基金项目资助(11511092)

摘　　要：在推广后的Black-Scholes模型框架基础上,探讨了不完全市场中金融资产价格受公司的盈利指标、通货膨胀率,外部经济因素等随机因素影响的最优投资与消费问题,运用鞅分析方法证明了受随机因素影响的投资与消费模型中最优投资与消费策略的存在性,进一步利用鞅分解定理表示出期末终端财富的表达式.同时,以效用函数为决策依据,对HARA效用函数给出了投资者具体的投资与消费策略,从而为投资者实现期末终端财富最大化提供了方法和依据.We discuss the problem of optimal investment and consumption in the incomplete markets in which the finace asset pricing is influenced outer economic factors that the payoff index,inflation rate, and use the martingale analysis method to prove the exist of optimal strategies of investment and consumption in the investment and consumption model which is influenced of random factors, and make use of the martingale decomposition theorem to give the expression of termind wealth, simultaneity according as utility function for the HARA utility function give the concrete investment and consumption strategies, thereby provide the method and gist in order to actualize maximal termind wealth.

关 键 词：鞅分析 效用函数 不完全市场 最优投资与消费 

分 类 号：O211.6[理学—概率论与数理统计] F830.59[理学—数学]